Сандық өрнектерді тепе-тең түрлендіру (Рустюмова 1.1.1А (1-16)) ∞ QAZ MATH

+/- – Есептің жауабын көрсету/көрсетпеу.

▲/▼ – Жауап орнын жасыру/шығару

× – Сұрақты алып тастау.

Есептеңіз.

№ 1.1 Есептеңіз: ${3,7 – (1,133:1,1 – 1,2):}$ ${( – 0,02) \cdot 0,2}$

Шешуі: $${1,133:1,1 = \dfrac{{1133}}{{1000}} \cdot \dfrac{{10}}{{11}} = \dfrac{{1100 + 33}}{{100 \cdot 11}} = \dfrac{{103}}{{100}} = 1,03}$$ $${1,03 – 1,2 = – 0,17}$$ $${ – 0,17:( – 0,02) \cdot 0,2 = \dfrac{{17}}{{100}} \cdot \dfrac{{100}}{2} \cdot \dfrac{2}{{10}} = 1,7}$$ $${3,7 – 1,7 = 2}$$

№ 1.2 Есептеңіз: $\dfrac{{(4,3 – 0,64:1,6) \cdot 0,25}}{{\dfrac{{25}}{{16}}:2,5 + 0,375 \cdot \dfrac{1}{3}}}$

Шешуі: $$ = \dfrac{{(4,3 – 0,4) \cdot 0,25}}{{\dfrac{{25}}{{16}} \cdot \dfrac{2}{5} + \dfrac{3}{8} \cdot \dfrac{1}{3}}} = \dfrac{{3,9 \cdot 0,25}}{{\dfrac{5}{8} + \dfrac{1}{8}}} = \dfrac{{3,9 \cdot \dfrac{1}{4}}}{{\dfrac{6}{8}}} = \dfrac{{3,9 \cdot \dfrac{1}{4}}}{{\dfrac{3}{4}}} = 1,3$$

№ 1.3 Есептеңіз: ${2\dfrac{2}{3}:1\dfrac{7}{9} + \dfrac{{55}}{{84}}:\left( {\dfrac{{43}}{{63}} – \dfrac{{23}}{{36}}} \right)}$

Шешуі: $${ = \dfrac{8}{3}:\dfrac{{16}}{9} + \dfrac{{55}}{{84}}:\left( {\dfrac{{43}}{{9 \cdot 7}} – \dfrac{{23}}{{9 \cdot 4}}} \right) = \dfrac{8}{3} \cdot \dfrac{9}{{16}} + \dfrac{{55}}{{84}}:\dfrac{{43 \cdot 4 – 23 \cdot 7}}{{9 \cdot 7 \cdot 4}} = }$$ $${ = \dfrac{3}{2} + \dfrac{{55}}{{84}}:\dfrac{{9 \cdot 7 \cdot 4}}{{172 – 161}} = \dfrac{3}{2} + \dfrac{{55}}{3} \cdot \dfrac{9}{{11}} = \dfrac{3}{2} + 15 = 16,5}$$

№ 1.4 Есептеңіз: ${5\dfrac{5}{7}:\dfrac{8}{{21}} + 1\dfrac{8}{{13}} \cdot \left( {\dfrac{{43}}{{56}} – \dfrac{{11}}{{24}}} \right)}$

Шешуі: $${ = \dfrac{{40}}{7} \cdot \dfrac{{21}}{8} + \dfrac{{21}}{{13}} \cdot \left( {\dfrac{{43}}{{8 \cdot 7}} – \dfrac{{11}}{{8 \cdot 3}}} \right) = 15 + \dfrac{{21}}{{13}} \cdot \left( {\dfrac{{43 \cdot 3 – 7 \cdot 11}}{{8 \cdot 7 \cdot 3}}} \right) = }$$ $${ = 15 + \dfrac{{21}}{{13}} \cdot \dfrac{{52}}{{8 \cdot 21}} = 15 + \dfrac{4}{8} = 15,5}$$

№ 1.5 Есептеңіз: ${\left( {\dfrac{{41}}{{18}} – \dfrac{{17}}{{36}}} \right) \cdot \dfrac{{18}}{{65}} +}$ $ {\left( {\dfrac{8}{7} – \dfrac{{23}}{{49}}} \right):\dfrac{{99}}{{49}} + \dfrac{7}{6}}$

Шешуі: $${ = \dfrac{{41 \cdot 2 – 17}}{{36}} \cdot \dfrac{{18}}{{65}} + \dfrac{{8 \cdot 7 – 23}}{{49}} \cdot \dfrac{{49}}{{99}} + \dfrac{7}{6} = \dfrac{{18}}{{36}} + \dfrac{{33}}{{99}} + \dfrac{7}{6} = }$$ $${ = \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{7}{6} = \dfrac{{3 + 2 + 7}}{6} = \dfrac{{12}}{6} = 2}$$

№ 1.6 Есептеңіз: ${\left( {\dfrac{1}{2} + 0,125 – \dfrac{1}{6}} \right) }$ ${\cdot \left( {6,4:\dfrac{{80}}{3}} \right) + \dfrac{1}{8}}$

Шешуі: $${ = \left( {\dfrac{1}{2} + \dfrac{1}{8} – \dfrac{1}{6}} \right) \cdot \left( {\dfrac{{32}}{5} \cdot \dfrac{3}{{80}}} \right) + \dfrac{1}{8} = }$$ $${ = \dfrac{{24 + 6 – 8}}{{48}} \cdot \dfrac{6}{{25}} + \dfrac{1}{8} = \dfrac{{22}}{{48}} \cdot \dfrac{6}{{25}} + \dfrac{1}{8} = \dfrac{{11}}{{4 \cdot 25}} + \dfrac{1}{8} = }$$ $${ = \dfrac{{110}}{{1000}} + \dfrac{{125}}{{1000}} = 0,235}$$

№ 1.7 Есептеңіз: ${\left( {6\dfrac{2}{3} + 2\dfrac{4}{{15}} + 5\dfrac{1}{2}} \right):\dfrac{1}{{15}} – }$ ${30:\dfrac{5}{{28}}}$

Шешуі: $${ = \left( {\dfrac{{20}}{3} + \dfrac{{34}}{{15}} + \dfrac{{11}}{2}} \right) \cdot 15 – 30 \cdot \dfrac{{28}}{5} = }$$ $${ = \dfrac{{20 \cdot 10 + 2 \cdot 34 + 15 \cdot 11}}{{30}} \cdot 15 – 6 \cdot 28 = }$$ $${\dfrac{{268 + 165}}{2} – 168 = 134 + \dfrac{{165}}{2} – 168 = 82\dfrac{1}{2} – 34 = 48\dfrac{1}{2}}$$

№ 1.8 Есептеңіз: ${\left( {13\dfrac{{13}}{{15}} – 12\dfrac{3}{{20}} – 5\dfrac{4}{{45}} – 0,85} \right) \cdot 3}$

Шешуі: $${ = \left( {3\dfrac{{13}}{{15}} – 5\dfrac{4}{{45}} – \left( {12\dfrac{3}{{20}} + \dfrac{{85}}{{100}}} \right)} \right) \cdot 3 = \left( {3\dfrac{{39}}{{45}} – 4\dfrac{{49}}{{45}} – \left( {12\dfrac{3}{{20}} + \dfrac{{17}}{{20}}} \right)} \right) \cdot 3 = }$$ $${ = \left( { – 1\dfrac{{10}}{{45}} – 13} \right) \cdot 3 = – 14\dfrac{2}{9} \cdot 3 = – \dfrac{{126 + 2}}{9} \cdot 3 = – \dfrac{{128}}{3} = – 42\dfrac{2}{3}}$$

№ 1.9 Есептеңіз: ${ – 7,8 – 1,3 \cdot (19,6:1,4 – 20)}$

Шешуі: $${ = – 7,8 – 1,3 \cdot (14 – 20) = – 7,8 – 1,3 \cdot ( – 6) = }$$ $${ = – 7,8 + 7,8 = 0}$$

№ 1.10 Есептеңіз: ${\left( {3,24:\dfrac{9}{7} – 3\dfrac{1}{5}:1\dfrac{1}{3}} \right):0,9}$

Шешуі: $${ = \left( {3,24 \cdot \dfrac{7}{9} – \dfrac{{16}}{5} \cdot \dfrac{3}{4}} \right) \cdot \dfrac{{10}}{9} = \left( {\dfrac{{324}}{{100}} \cdot \dfrac{7}{9} – \dfrac{{12}}{5}} \right) \cdot \dfrac{{10}}{9} = }$$ $${ = \left( {\dfrac{{81}}{{25}} \cdot \dfrac{7}{9} – \dfrac{{12}}{5}} \right) \cdot \dfrac{{10}}{9} = \left( {\dfrac{{63}}{{25}} – \dfrac{{12 \cdot 5}}{{25}}} \right) \cdot \dfrac{{10}}{9} = \dfrac{3}{{25}} \cdot \dfrac{{10}}{9} = \dfrac{2}{{15}}}$$

№ 1.11 Өрнектің мәніне кері санды табыңыз: $\dfrac{5}{{14}}:\dfrac{{25}}{{72}} \cdot \dfrac{7}{{12}}:\dfrac{5}{{36}} \cdot 2\dfrac{1}{{12}}$

Шешуі: $$ = \dfrac{5}{{14}} \cdot \dfrac{{72}}{{25}} \cdot \dfrac{7}{{72}} \cdot \dfrac{{36}}{5} \cdot \dfrac{{25}}{{12}} = \dfrac{{18}}{2} = 9$$ Кері сан : $\dfrac{1}{9}$

№ 1.12 Мына санды периодты ондық ондық бөлшек түрінде жазыңыз: $\dfrac{{53}}{{22}}$

Шешуі: $$\dfrac{{53}}{{22}} = 2,40909… = 2,4\left( {09} \right)$$